Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
sqrt(cos(x)+sin(2*x)+sin(1/(x^2)))+sin(1/(x^2))
¿Cómo vas a descomponer esta sqrt(cos(x)+sin(2*x)+sin(1/(x^2)))+sin(1/(x^2)) expresión en fracciones?
Solución
Ha introducido
[src]
_____________________________
/ /1 \ /1 \
/ cos(x) + sin(2*x) + sin|--| + sin|--|
/ | 2| | 2|
\/ \x / \x /
$$\sqrt{\left(\sin{\left(2 x \right)} + \cos{\left(x \right)}\right) + \sin{\left(\frac{1}{x^{2}} \right)}} + \sin{\left(\frac{1}{x^{2}} \right)}$$
sqrt(cos(x) + sin(2*x) + sin(1/(x^2))) + sin(1/(x^2))
Simplificación general
[src]
_____________________________
/ /1 \ /1 \
/ cos(x) + sin|--| + sin(2*x) + sin|--|
/ | 2| | 2|
\/ \x / \x /
$$\sqrt{\sin{\left(\frac{1}{x^{2}} \right)} + \sin{\left(2 x \right)} + \cos{\left(x \right)}} + \sin{\left(\frac{1}{x^{2}} \right)}$$
sqrt(cos(x) + sin(x^(-2)) + sin(2*x)) + sin(x^(-2))
Respuesta numérica
[src]
(cos(x) + sin(1/(x^2)) + sin(2*x))^0.5 + sin(1/(x^2))
(cos(x) + sin(1/(x^2)) + sin(2*x))^0.5 + sin(1/(x^2))
Unión de expresiones racionales
[src]
_____________________________
/ /1 \ /1 \
/ cos(x) + sin|--| + sin(2*x) + sin|--|
/ | 2| | 2|
\/ \x / \x /
$$\sqrt{\sin{\left(\frac{1}{x^{2}} \right)} + \sin{\left(2 x \right)} + \cos{\left(x \right)}} + \sin{\left(\frac{1}{x^{2}} \right)}$$
sqrt(cos(x) + sin(x^(-2)) + sin(2*x)) + sin(x^(-2))
Denominador común
[src]
_____________________________
/ /1 \ /1 \
/ cos(x) + sin|--| + sin(2*x) + sin|--|
/ | 2| | 2|
\/ \x / \x /
$$\sqrt{\sin{\left(\frac{1}{x^{2}} \right)} + \sin{\left(2 x \right)} + \cos{\left(x \right)}} + \sin{\left(\frac{1}{x^{2}} \right)}$$
sqrt(cos(x) + sin(x^(-2)) + sin(2*x)) + sin(x^(-2))
Combinatoria
[src]
_____________________________
/ /1 \ /1 \
/ cos(x) + sin|--| + sin(2*x) + sin|--|
/ | 2| | 2|
\/ \x / \x /
$$\sqrt{\sin{\left(\frac{1}{x^{2}} \right)} + \sin{\left(2 x \right)} + \cos{\left(x \right)}} + \sin{\left(\frac{1}{x^{2}} \right)}$$
sqrt(cos(x) + sin(x^(-2)) + sin(2*x)) + sin(x^(-2))
Potencias
[src]
__________________________________________________________
/ / -I I \ / -I I \
/ | --- --| | --- --|
/ | 2 2| | 2 2|
/ I*x -I*x | x x | / -2*I*x 2*I*x\ | x x |
/ e e I*\- e + e / I*\- e + e / I*\- e + e /
/ ---- + ----- - ---------------- - ---------------------- - ----------------
\/ 2 2 2 2 2
$$- \frac{i \left(e^{\frac{i}{x^{2}}} - e^{- \frac{i}{x^{2}}}\right)}{2} + \sqrt{- \frac{i \left(e^{\frac{i}{x^{2}}} - e^{- \frac{i}{x^{2}}}\right)}{2} - \frac{i \left(e^{2 i x} - e^{- 2 i x}\right)}{2} + \frac{e^{i x}}{2} + \frac{e^{- i x}}{2}}$$
_____________________________
/ /1 \ /1 \
/ cos(x) + sin|--| + sin(2*x) + sin|--|
/ | 2| | 2|
\/ \x / \x /
$$\sqrt{\sin{\left(\frac{1}{x^{2}} \right)} + \sin{\left(2 x \right)} + \cos{\left(x \right)}} + \sin{\left(\frac{1}{x^{2}} \right)}$$
sqrt(cos(x) + sin(x^(-2)) + sin(2*x)) + sin(x^(-2))
Compilar la expresión
[src]
_____________________________
/ /1 \ /1 \
/ cos(x) + sin|--| + sin(2*x) + sin|--|
/ | 2| | 2|
\/ \x / \x /
$$\sqrt{\sin{\left(2 x \right)} + \sin{\left(\frac{1}{x^{2}} \right)} + \cos{\left(x \right)}} + \sin{\left(\frac{1}{x^{2}} \right)}$$
sqrt(cos(x) + sin(1/(x^2)) + sin(2*x)) + sin(1/(x^2))
Denominador racional
[src]
_____________________________
/ /1 \ /1 \
/ cos(x) + sin|--| + sin(2*x) + sin|--|
/ | 2| | 2|
\/ \x / \x /
$$\sqrt{\sin{\left(\frac{1}{x^{2}} \right)} + \sin{\left(2 x \right)} + \cos{\left(x \right)}} + \sin{\left(\frac{1}{x^{2}} \right)}$$
sqrt(cos(x) + sin(x^(-2)) + sin(2*x)) + sin(x^(-2))
Parte trigonométrica
[src]
_____________________________________________
/ / 1 \ / 1 \
/ 2/x\ 2*cot|----| 2*cot|----|
/ -1 + cot |-| | 2| | 2|
/ \2/ 2*cot(x) \2*x / \2*x /
/ ------------ + ----------- + -------------- + --------------
/ 2/x\ 2 2/ 1 \ 2/ 1 \
/ 1 + cot |-| 1 + cot (x) 1 + cot |----| 1 + cot |----|
/ \2/ | 2| | 2|
\/ \2*x / \2*x /
$$\sqrt{\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{2 \cot{\left(x \right)}}{\cot^{2}{\left(x \right)} + 1} + \frac{2 \cot{\left(\frac{1}{2 x^{2}} \right)}}{\cot^{2}{\left(\frac{1}{2 x^{2}} \right)} + 1}} + \frac{2 \cot{\left(\frac{1}{2 x^{2}} \right)}}{\cot^{2}{\left(\frac{1}{2 x^{2}} \right)} + 1}$$
_____________________________
/ /1 \ /1 \
/ cos(x) + sin|--| + sin(2*x) + sin|--|
/ | 2| | 2|
\/ \x / \x /
$$\sqrt{\sin{\left(\frac{1}{x^{2}} \right)} + \sin{\left(2 x \right)} + \cos{\left(x \right)}} + \sin{\left(\frac{1}{x^{2}} \right)}$$
_____________________________
/ 1 1 1 1
/ ------- + -------- + ------ + -------
/ /1 \ csc(2*x) sec(x) /1 \
/ csc|--| csc|--|
/ | 2| | 2|
\/ \x / \x /
$$\sqrt{\frac{1}{\sec{\left(x \right)}} + \frac{1}{\csc{\left(2 x \right)}} + \frac{1}{\csc{\left(\frac{1}{x^{2}} \right)}}} + \frac{1}{\csc{\left(\frac{1}{x^{2}} \right)}}$$
_______________________________________
/ /1 pi\ / pi\ /1 pi\
/ cos(x) + cos|-- - --| + cos|2*x - --| + cos|-- - --|
/ | 2 2 | \ 2 / | 2 2 |
\/ \x / \x /
$$\sqrt{\cos{\left(x \right)} + \cos{\left(- \frac{\pi}{2} + \frac{1}{x^{2}} \right)} + \cos{\left(2 x - \frac{\pi}{2} \right)}} + \cos{\left(- \frac{\pi}{2} + \frac{1}{x^{2}} \right)}$$
__________________________________
/ 1 1 1 1
/ ------- + -------- + ----------- + -------
/ /1 \ csc(2*x) /pi \ /1 \
/ csc|--| csc|-- - x| csc|--|
/ | 2| \2 / | 2|
\/ \x / \x /
$$\sqrt{\frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}} + \frac{1}{\csc{\left(2 x \right)}} + \frac{1}{\csc{\left(\frac{1}{x^{2}} \right)}}} + \frac{1}{\csc{\left(\frac{1}{x^{2}} \right)}}$$
__________________________________
/ /1 \ / pi\ /1 \
/ sin|--| + sin(2*x) + sin|x + --| + sin|--|
/ | 2| \ 2 / | 2|
\/ \x / \x /
$$\sqrt{\sin{\left(\frac{1}{x^{2}} \right)} + \sin{\left(2 x \right)} + \sin{\left(x + \frac{\pi}{2} \right)}} + \sin{\left(\frac{1}{x^{2}} \right)}$$
____________________________________________
/ / 1 \ / 1 \
/ 2/x\ 2*tan|----| 2*tan|----|
/ 1 - tan |-| | 2| | 2|
/ \2/ 2*tan(x) \2*x / \2*x /
/ ----------- + ----------- + -------------- + --------------
/ 2/x\ 2 2/ 1 \ 2/ 1 \
/ 1 + tan |-| 1 + tan (x) 1 + tan |----| 1 + tan |----|
/ \2/ | 2| | 2|
\/ \2*x / \2*x /
$$\sqrt{\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{2 \tan{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1} + \frac{2 \tan{\left(\frac{1}{2 x^{2}} \right)}}{\tan^{2}{\left(\frac{1}{2 x^{2}} \right)} + 1}} + \frac{2 \tan{\left(\frac{1}{2 x^{2}} \right)}}{\tan^{2}{\left(\frac{1}{2 x^{2}} \right)} + 1}$$
_______________________________________
/ 1 1 1 1
/ ------ + ------------ + ------------- + ------------
/ sec(x) /1 pi\ / pi\ /1 pi\
/ sec|-- - --| sec|2*x - --| sec|-- - --|
/ | 2 2 | \ 2 / | 2 2 |
\/ \x / \x /
$$\sqrt{\frac{1}{\sec{\left(2 x - \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(- \frac{\pi}{2} + \frac{1}{x^{2}} \right)}} + \frac{1}{\sec{\left(x \right)}}} + \frac{1}{\sec{\left(- \frac{\pi}{2} + \frac{1}{x^{2}} \right)}}$$
sqrt(1/sec(x) + 1/sec(x^(-2) - pi/2) + 1/sec(2*x - pi/2)) + 1/sec(x^(-2) - pi/2)